Related papers: Independent Component Analysis via Distance Covari…
Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable. Here, we first propose a new intuitive principle of unsupervised deep…
In this paper we use a well know method in statistics, the $\delta$-method, to provide an asymptotic distribution for the Mutual Information, and construct and independence test based on it. Interesting connections are found with the…
The brain effortlessly solves blind source separation (BSS) problems, but the algorithm it uses remains elusive. In signal processing, linear BSS problems are often solved by Independent Component Analysis (ICA). To serve as a model of a…
The advancement in the field of data science especially in machine learning along with vast databases of variable star projects like the Optical Gravitational Lensing Experiment (OGLE) encourages researchers to analyse as well as classify…
Recently, nonlinear ICA has surfaced as a popular alternative to the many heuristic models used in deep representation learning and disentanglement. An advantage of nonlinear ICA is that a sophisticated identifiability theory has been…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
We propose a family of tests of the validity of the assumptions underlying independent component analysis methods. The tests are formulated as L2-type procedures based on characteristic functions and involve weights; a proper choice of…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures…
Given an iid sequence of pairs of stochastic processes on the unit interval we construct a measure of independence for the components of the pairs. We define distance covariance and distance correlation based on approximations of the…
Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…
With the emergence of wireless sensor networks (WSNs), many traditional signal processing tasks are required to be computed in a distributed fashion, without transmissions of the raw data to a centralized processing unit, due to the limited…
We study the problem of unsupervised representation learning in slightly misspecified settings, and thus formalize the study of robustness of nonlinear representation learning. We focus on the case where the mixing is close to a local…
We study optimization methods for solving the maximum likelihood formulation of independent component analysis (ICA). We consider both the the problem constrained to white signals and the unconstrained problem. The Hessian of the objective…
There are a multitude of methods to perform multi-set correlated component analysis (MCCA), including some that require iterative solutions. The methods differ on the criterion they optimize and the constraints placed on the solutions. This…
We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…
This study utilizes Independent Component Analysis (ICA) to unveil a consistent semantic structure within embeddings of words or images. Our approach extracts independent semantic components from the embeddings of a pre-trained model by…
Latent component identification from unknown nonlinear mixtures is a foundational challenge in machine learning, with applications in tasks such as disentangled representation learning and causal inference. Prior work in nonlinear…
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
Advances in data collection are producing growing volumes of temporal count observations, making adapted modeling increasingly necessary. In this work, we introduce a generative framework for independent component analysis of temporal count…